All Bilaam's power and genius ultimately led to him doing the opposite of what he and King Balak plotted to do: Rather than cursing Am Yisrael, Bilaam blessed them.
While rationalist thought attributes other explanations for Bilaam's power and considers any apparent occult powers as wholly 3-dimensional tricks of illusion, the majority of sources throughout Chazal acknowledge the powers and abilities we now term as supernatural.
Unfortunately, when people display psychic powers or supernatural abilities, others see this as evidence of deeper wisdom & elevated spirituality—and this assumption is simply not true.
One can access these powers and still lack the wisdom of knowing there is One Source for everything, One Power, One God.
A truly spiritual person recognizes the One & Only God.
A truly spiritually enlightened person, whether Jewish or not, realizes that God gave Am Yisrael the Torah at Har Sinai—and that the Torah is True.
In contrast, these people with special powers almost always lack the wisdom to know how to behave morally and with integrity.
They possess brazenness, but no courage.
When push comes to shove, they fold.
In a fascinating Q&A, Rav Schwartz briefly explains how this works, its limitations, and the halachic boundaries when using psychic abilities (boldface & underline my own additions):
INTRUDING INTO ANOTHER’S PRIVACY THROUGH ESP [#18926]
I want to know if it’s “permitted” for a person who has “spiritual powers” [of ESP, extrasensory perception] to penetrate into another’s privacy [i.e. reading his thoughts and feelings and seeing into his spiritual level].
Assuming that we are talking about a person who has indeed been gifted with a spiritual ability to “see” certain things in others, is such a person allowed to make use of his ability to “see into” others, without asking their permission first?
There are some people who are able to leave their physical body, which is called “teleporting” – are such people able to have some kind of control over others or harm others?
Does G-d approve of such behavior, and will such a person be punished by Heaven for doing such a thing?
Are these people “allowed” to do this because they possess a high soul level?
And, how can a person protect his privacy from being invaded by such people (since he can’t see them)?
In our world of action, we are obligated in the 613 mitzvos of the Torah and in the 7 primary Rabbinical mitzvos, and in all of the commandments which we have received through tradition, as well as in all of the decrees and prohibitions that the Sages have enacted.
The more a person grows spiritually, the more “obligations” he will discover, which are on a more spiritual level, in addition to all that he is obligated in from the perspective of this lower world, the realm of action.
In the lower world, the world of action, it is forbidden for us to enter into another person’s property without permission – it is forbidden because it is stealing.
It is the same in the more spiritual dimensions:
Whenever a person enters into another’s “privacy,” this is called stealing, on a spiritual level.
As an example, a person gains spiritual merits as a result of doing mitzvos and positive deeds on this world.
These become his spiritual acquisitions.
Therefore, if a person is genuinely spiritual and he is truthful, he will not enter into another’s private “world,” and he will only do so within the context of halachah, integrity, and kindness to another.
However, there are some people who are found in the spiritual dimension, but they are only in the lower realm of the spiritual dimension, where there is a mixture of good and evil.
In the language of the Sages, this is referred to as “the world of exchanges.”
In such people, the “animal” layer of their souls (their nefesh habehaimis) is mixed into their spiritual powers [which causes their spirituality to be unrefined and lacking in truthfulness].
They have two problems:
They are found in a spiritual dimension which is unrefined, because they are at a dimension where there is a mixture of good and evil.
In addition, their very souls are unrefined: the “animal” layer of their soul has not yet been refined, so it is mixed into their spiritual world, and this causes them to be misled, according to their various interests.
Just as it is possible in the physical world to steal from another person, so is it possible to “steal” on a spiritual level from another person, by intruding into his privacy [i.e. entering into another’s thoughts and feelings without permission], when one is living at an unrefined spiritual place of existence.
And just as in the physical world each person has his own boundaries and capabilities, according to his own level, so does a person have emotional boundaries and limitations, physical boundaries and limitations, and financial boundaries and limitations.
And just as a person in the physical world can be harmed by another, so can a person be harmed by another, in the unrefined spiritual plane of existence.
However, the more that a person becomes attached to the Creator and believes in His total Divine Providence, to that extent, no created being can harm him on his own accord.
A person can only be harmed if G-d wills it.
The power of free choice that is given to a person is essentially if he will choose to connect or not to the lowly and unrefined forces in Creation, entering into a world where the “Destroyer” [the destroying angel, Satan] is given permission to destroy as it wishes.
For this reason, it is possible for a person to be harmed by one who has unrefined spiritual powers.
The other choice that a person has is the choice to connect himself to the Creator, and to have the pure belief in Him that “only He can do, has done, and will do, all actions.”